A postgraduate conference will be held on Monday April 6th. The morning schedule will consist of a series of talks. This is an opportunity for mathematics students to present their research to an audience of peers. Attendance by anyone other than postgraduate students is strictly by invitation only.

Posters will be exhibited on the university concourse throughout the conference.

All talks will be held in the McMunn Theatre on the university concourse.

This is joint work with RT Curtis. Exhibiting generating sets for groups that have an underlying highly symmetric combinatorial structure has proved extremely useful in providing new existence proofs for various groups (most notably the sporadic simple groups) and for providing a succinct means of representing their elements. Since it is naturally much easier to find symmetric generating sets for smaller groups than larger groups it is natural to seek means of extending symmetric generating sets to larger symmetric generating sets. In this talk we describe some previously used approaches to this problem to highlight their weeknesses before describing a new more flexable approach to this problem and giving an explicit example relating to the groups SU_3(2^r).

Why are some graphs easier to deal with than others for difficult algorithmic problems? Indeed, many NP-complete graph problems (such as finding a maximum independent vertex set) can be made polynomial-time solvable by restricting to an interesting subclass of all graphs. We will discuss strategies for determining whether a graph class is 'friendly' in this respect. We will also describe how to find minimal 'unfriendly' classes of graphs. The talk will concentrate on examples and graph-theoretical proofs, and it will be extremely light on the technical details of algorithms.

Morse Theory is a beautiful and helpful tool in Topology. In this talk, I will explain some theorems of Morse Theory that help us understand the topology of a compact manifold. I will try to give insight into the geometrical decomposition in cells of a compact manifold via Morse Theory. This talk will include examples to show how powerful Morse Theory can be.

We investigate the SL(2,R) invariant geodesic curves with the associated invariant distance function in parabolic geometry. Parabolic geometry naturally occurs as action of SL(2,R) on dual numbers and is placed in between the elliptic and the hyperbolic geometries (which arise from the action of SL(2,R) on complex and double numbers). Initially we attempt to use standard methods of finding geodesics but they lead to degeneracy in this set-up. Instead, by studying closely the two related hypercomplex numbers we discover a unified approach to a more exotic and less obvious dual number's case. With aid of common invariants we describe the possible distance functions that turn out to have some unexpected, interesting properties.

Neurons in the brain, especially nearby neurons, are often correlated, in the sense that activity in one set of neurons partially predicts the activity in another. Determining the correlation structure in large neural networks is critical for understanding everything from information storage to network dynamics to computing to learning in the brain. Historically, the main approach has been experimental, but the amount of data required to accurately assess correlations scales very badly with the number of neurons. We derive an expression which relates correlations to the network connectivity and single neuron properties.

Following a recent article of Goetz Pfeiffer that describes a mechanism for producing a quiver presentation of the descent algebra of a finite Coxeter group, we apply the method in the case of the Coxeter group of type A by representing the elements of Pfeiffer's presentation as sequences of binary trees. We intend to use the same method to calculate quiver presentations for the other infinite families of Coxeter groups.